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Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives. (Chinese) Zbl 1212.65342
Summary: A two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which modifies the well-known Darcy law. Using the relationship between Riemann-Liouville and Grünwald-Letnikov fractional derivatives, two modified alternating direction methods, a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence, of the two methods in a bounded domain are discussed. Finally, numerical results are given.
MSC:
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
65Z05Applications of numerical analysis to physics
76S05Flows in porous media; filtration; seepage